A truck ahead suddenly brakes. How much distance should you keep to avoid a collision — and does that safe distance depend on your speed?
Key idea
Position, Distance, and Displacement
1
Distance travelled
The entire path length covered — a scalar, magnitude only.
→
2
Displacement
The net change in position between two instants — a vector, with both magnitude and direction.
Key idea
A Ball Thrown Up and Caught Again
Distance and displacement are equal only when an object never turns back.
Thrown up, caught at the same spotTotal distance travelled = up + down (added together). Displacement = 0, since the ball ends up exactly where it started.
Key idea
Average Speed and Average Velocity
1
Average speed
Total distance ÷ time interval. A scalar — no direction.
→
2
Average velocity
Displacement ÷ time interval. A vector — direction matches the displacement. SI unit for both: m/s.
Key idea
Uniform and Non-uniform Motion
1
Uniform motion
Equal distances covered in equal time intervals — constant speed.
→
2
Non-uniform motion
Unequal distances covered in equal time intervals — changing speed.
Key idea
Average Acceleration
Average acceleration = change in velocity ÷ time interval. SI unit: m/s².
Speed and acceleration aren't the same
An object moving very fast at a constant velocity has zero acceleration — acceleration depends on how quickly velocity changes, not on speed itself.
Key idea
Position-Time Graphs
Constant velocity (straight line)
Changing velocity (curved line)
Key idea
Velocity-Time Graphs
Constant positive acceleration
Constant negative acceleration (braking)
Key idea
Slope and Area Under the Graph
1
The slope
On a position-time graph, slope = velocity. On a velocity-time graph, slope = acceleration.
→
2
The area
The area enclosed between a velocity-time graph's line and the time axis equals the displacement.
Key idea
The Three Kinematic Equations
u = initial velocity, v = final velocity, a = constant acceleration, t = time, s = displacement.
Equation | Relates
v = u + at
Final velocity to time
s = ut + ½at²
Displacement to time
v² = u² + 2as
Final velocity to displacement
Key idea
Motion in a Plane and Circular Motion
1
Two dimensions
Motion confined to a flat plane — like a kicked ball's path, or a vehicle overtaking another.
→
2
Circular motion
Movement along a circular path. Distance in one revolution = 2πR (circumference); displacement after one full revolution = 0.
Key idea
Uniform Circular Motion Is Still Accelerated
Uniform circular motion means constant speed along a circular path.
Direction keeps changing
Even though speed never changes, the direction of velocity constantly does — so the motion is still accelerated, just from a change in direction, not speed.
Chapter · Key terms to remember
Key Terms
Distance / Displacement
Total path length / net change in position.
Scalar / Vector
Magnitude only / magnitude and direction.
Average speed / velocity
Distance / time / displacement / time.
Chapter · Key terms to remember
More Key Terms
Uniform / Non-uniform motion
Constant speed / changing speed.
Average acceleration
Change in velocity ÷ time interval.
Slope
Velocity on a position-time graph; acceleration on a velocity-time graph.
Chapter · Key terms to remember
More Key Terms
Kinematic equations
v=u+at, s=ut+½at², v²=u²+2as.
Uniform circular motion
Circular motion at constant speed.
Questions for your notebook
Write these down, then discuss
1
My father walked 250 m from home to a shop, came back for a forgotten bag, went to the shop again, bought provisions, and came home. What was the total distance travelled, and his displacement from home?
2
A student runs from the ground floor to the 4th floor to fetch a book (3 m per floor), then comes down to the 2nd floor classroom. Find (i) total vertical distance, (ii) displacement from the start.
3
A girl riding a scooter sees a constant speedometer reading. Could her scooter still be accelerating? How?
Project as-is — students copy the questions, then the class discusses answers together.